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Search: id:A064191
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| A064191 |
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Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers. |
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+0
2
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| 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 9, 4, 5, 2, 1, 21, 9, 12, 5, 3, 1, 51, 21, 30, 12, 9, 3, 1, 127, 51, 76, 30, 25, 9, 4, 1, 323, 127, 196, 76, 69, 25, 14, 4, 1, 835, 323, 512, 196, 189, 69, 44, 14, 5, 1, 2188, 835, 1353, 512, 518, 189, 133, 44, 20, 5, 1, 5798, 2188, 3610, 1353
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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This triangle appears on page 9 of the linked reference and is defined by Corollary 2.4.
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LINKS
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J. L. Arregui, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles.
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FORMULA
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T(n, 0) = sum(T(n-1, k) : k = 0, ..., n-1). For k even, 0 < k <= n, T(n, k) = sum(T(n-1, j) : j = k-1, ..., n-1). For k odd, 0 < k <= n, T(n, k) = T(n-1, k-1). - David Wasserman (wasserma(AT)spawar.navy.mil), Jul 15 2002
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EXAMPLE
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1; 1,1; 2,1,1; 4,2,2,1; ...
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CROSSREFS
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First column gives A001006.
Sequence in context: A156861 A122773 A029268 this_sequence A127420 A129033 A054090
Adjacent sequences: A064188 A064189 A064190 this_sequence A064192 A064193 A064194
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jul 15 2002
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